Basic Algebra : Log

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Johnny Yi 6 years, 3 months ago

Created this as a copy of Harry's copy of David's copy of Using the Logarithm Equivalence

$\log_ba=c \Longleftrightarrow a=b^c$ .

Name	Status	Author	Last Modified
Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Hannah Aldous	20/11/2019 14:45
Inbbavathie's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Inbbavathie Ravi	24/07/2017 03:49
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Ida Landgärds	09/05/2018 06:55
spørsmål 2	Ready to use	Ida Landgärds	16/04/2021 05:04
Logarithms [L6]	draft	Abbi Mullins	24/07/2018 14:52
David's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	David Martin	30/07/2018 14:34
Harry's copy of David's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Harry Flynn	15/11/2018 10:33
Basic Algebra : Log	draft	Johnny Yi	23/01/2019 05:00
Maria's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Maria Aneiros	29/05/2019 06:58
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Xiaodan Leng	11/07/2019 00:16
Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Xiaodan Leng	11/07/2019 01:47
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Wan Mekwi	13/10/2020 13:19
Ugur's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Ugur Efem	12/01/2022 11:45

There are 31 other versions that do you not have access to.

Question statement

You may use the following equivalence to solve problems in this page.

$\log_ba=c \Longleftrightarrow a=b^c\text{.}$

Give any introductory information the student needs.

			Name	Type	Generated Value

g3	integer	2
g2	integer	3
g4	integer	6
g1	integer	9

			Name	Type	Generated Value

			h1	integer	2
			h2	integer	4

			Name	Type	Generated Value

f	integer	4
f2	integer	3
f1	integer	3
f3	integer	6
f4	integer	5
f5	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10except g1 g2)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Choose several from a list

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Rearrange the equation to find $x$ .

$\log_\var{f}(x)=\var{f1}$

$x=$ Unnamed gap

Advice

a)

We can rearrange logarithms using indices.

$\log_ba=c \Longleftrightarrow a=b^c$

Using this equivalence we can rewrite $\log_\var{f}x=\var{f1}$ .

$\begin{align} x&= \var{f}^\var{f1} \\ &=\var{f^f1} \end{align}$

b)

We can use the equivalence to rewrite our equation.

$\log_ba=c \Longleftrightarrow a=b^c$

We can write out our values to makes it easier.

$\begin{align} a&=x \\ b&=\var{g1}\\ c&=y+\var{g2} \end{align}$

Then we can write out our equation in the required form.

$x=\var{g1}^{y+\var{g2}}$

c)

We can use the same equivalence as in part b).

$\log_ba=c \Longleftrightarrow a=b^c$

We have

$\begin{align} a&=y+\var{h1} \\ b&=x\\ c&=\var{h2}\text{.} \\ \\ \log_{x}(y+\var{h1}) &= \var{h2} \\ \implies y+\var{h1} &= x^{\var{h2}} \\ x &= (y+\var{h1})^{\frac{1}{\var{h2}}} \end{align}$

d)

The two in this list that don't equal $x$ are $\log_e(x)$ and $\log_{10}(x)$ .

$\begin{align} \log_e(x)&=\ln(x)\\ \log_{10}(x)&=\log(x)\text{.} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose several from a list
Choose several from a list		Hasn't run yet

This question is used in the following exams:

Portfolio - Logs and Indices by Paul Finley in Paul's workspace.
Diagnostic Test For MATH1013 at ANU by Johnny Yi in Johnny's workspace.
Logarithms by Leonardo Juliano in BiomedSkills.
2020 Diagnostic Test For MATH1013 at ANU by Griff Ware in Griff's workspace.
Diagnostic Test For MATH1013 at ANU by Johnny Yi in Diagnostic Test Materials.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Johnny Yi 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Error

Basic Algebra : Log

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Johnny Yi 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`